Flexible Discriminant Analysis by Optimal Scoring

Abstract

Fisher's linear discriminant analysis is a valuable tool for multigroup classification. With a large number of predictors, one can find a reduced number of discriminant coordinate functions that are “optimal” for separating the groups. With two such functions, one can produce a classification map that partitions the reduced space into regions that are identified with group membership, and the decision boundaries are linear. This article is about richer nonlinear classification schemes. Linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups. In this paper, we obtain nonparametric versions of discriminant analysis by replacing linear regression by any nonparametric regression method. In this way, any multiresponse regression technique (such as MARS or neural networks) can be postprocessed to improve its classification performance.